Magnetic field-induced modification of selection rules for Rb D2 line monitored by selective reflection from a vapor nanocell

Abstract

Magnetic field-induced giant modification of the probabilities of five transitions of 5S 1/2 , Fg = 2 → 5P 3/2 , Fe = 4 of 85 Rb and three transitions of 5S 1/2 , Fg = 1 → 5P 3/2 , Fe = 3 of 87 Rb forbidden by selection rules for zero magnetic field has been observed experimentally and described theoretically for the first time. For the case of excitation with circularly-polarized (σ + ) laser radiation, the probability of Fg = 2, mF = −2 → Fe = 4, mF = −1 transition becomes the largest among the seventeen transitions of 85 Rb Fg = 2 → Fe = 1, 2, 3, 4 group, and the probability of Fg = 1, mF = −1 → Fe = 3, mF = 0 transition becomes the largest among the nine transitions of 87 Rb Fg = 1 → Fe = 0, 1, 2, 3 group, in a wide range of magnetic field 200 -1000 G. Complete frequency separation of individual Zeeman components was obtained by implementation of derivative selective reflection technique with a 300 nm-thick nanocell filled with Rb, allowing formation of narrow optical resonances. Possible applications are addressed. The theoretical model is perfectly consistent with the experimental results.

The theory of selective reflection for a Fabry–Perot interferometer

“…This problem will be solved in the next section and we will compare our obtained formula for the reflection coefficient (22) with the classical one (7). Also, we will show that the first term of our approximate solution (20) has the same property as mentioned in (8).…”

Proof of the feasibility of a nanocell-based wide-range optical magnetometer

“…As one can see from Eq. (19) in [22], the accounting of the atomic velocity distribution in the NC for calculating SR spectrum can be extremely time consuming, as it is not possible to get analytic solutions. However, assuming that all the transitions in the spectrum have the same lineshape (which in the case of a NC is neither Loretzian/Gaussian nor Voigt), the selective reflection signal (Eq.…”

“…The lineshape S(ω, , Γ) of each individual transitions was pre-calculated using successively Eqs. (19), (18) and (14) from [22], setting µ eg = 1 and ∆ = 0, while the cell thickness = 490 ± 10 nm and the linewidth Γ = 50 ± 5 MHz were fit to that of a recorded experimental Rb D 2 spectrum (without magnetic field). This simplifications lead to a large enhancement of the calculations speed and, in this way, we estimate the calculation time to be reduced by a factor 100.…”

Hyperfine Paschen–Back regime of potassium D2 line observed by Doppler-free spectroscopy

“…For this reason, we call them"initially forbidden further allowed" (IFFA) transitions. Note that there is another type of "forbidden" transitions, so-called magnetically induced (MI) transitions since they appear only with the presence of B-field and verify the selection rule ∆F = F e − F g = ±2; particularly, the groups of transitions F g = 2 → F e = 4 (Rb D 2 line) and F g = 3 → F e = 5 (Cs D 2 line) have been respectively studied in [19,26]. For strong magnetic fields B ≫ B 0 the probabilities of MI transitions tend to zero, contrary to the one of the IFFA transitions that asymptotically tend to its maximum with increasing B-field (see Fig.…”